Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Frequency-selective effective model of driven multilevel systems in gate-defined quantum dots

Yuan Lin Zhou, Si‐Si Gu, Ke Wang, Gang Cao, Xuedong Hu, Ming Gong, Hai-Ou Li, Guo‐Ping Guo

Published Oct 19, 2021• 1 citation
OpenAlex

Abstract

Landau-Zener-St\uckelberg (LZS) interference is a common tool to study various quantum systems. When system is driven forth and back through anticrossings, phases are accumulated coherently, and results in constructive or destructive interference. LZS are widely demonstrated in two-level systems and multilevel systems. Nonetheless, multilevel physics in LZS interference of a multilevel system remains unexplored, since in most of the cases, influence of each anticrossing can be treated separately, thus two-level model is sufficient. Here, we investigate the LZS interference of multilevel systems in quantum dots (QDs), and propose a scheme to realize an effective model from the complicated energy levels. By employing this model, we study the physics in multilevel system such as Autler-Townes splitting (ATS), electromagnetically induced transparency and coherent population trapping (CPT) etc., and reveal their unique behaviors in our scheme. Specifically, possible improvement for present two-qubit gate in QDs and noise-robust quantum gates are proposed. The theoretical consideration we present is rather general, and thus is in principle valid for other quantum systems with the similar energy structure.

Related papers

Landau-Zener-Stückelberg interference in coherent charge oscillations of a one-electron double quantum dot

Takeshi Ota, Kenichi Hitachi, Koji Muraki

Landau-Zener (LZ) transition has received renewed interest as an alternative approach to control single-qubit states. An LZ transition occurs when a system passes through an avoided crossing that arises from quantum mechanical coupling of two levels, taking the system to a coherent superposition of the two states. Then, multiple LZ transitions induce interference known as Landau-Zener-Stückelberg (LZS) interference whose amplitude strongly depends on the velocity or adiabaticity of the passage. Here, we study the roles of LZ transitions and LZS interference in coherent charge oscillations of a one-electron semiconductor double quantum dot by time-domain experiments using standard rectangular voltage pulses. By employing density matrix simulations, we show that, in the standard setup using rectangular pulses, even a small distortion of the pulse can give rise to LZ transitions and hence LZS interference, which significantly enhances the measured oscillation amplitude. We further show experimentally that the nature of the coherent charge oscillations changes from Rabi-type to LZS oscillations with increasing pulse distortion. Our results thus demonstrate that it is essential to take into account LZS interference for both precise control of charge qubits and correct interpretation of measurement results.

Scientific Reports•Mar 29, 2018•16 citations

Multiple Landau-Zener crossings and quantum interference in atoms driven by phase modulated fields

Harshawardhan Wanare, G. S. Agarwal

The excitation amplitude after multiple crossings is not a mere product of Landau-Zener transition probabilities at each crossing, due to coherent evolution of the system in between crossings. In the three-level ladder system, the trapping of population by frequency modulated fields ensures coherent evolution, and inclusion of phase effects for population redistribution after multiple crossings becomes necessary. The relative phase accumulated by various adiabatic states as they evolve along different paths is tailored to show the existence of quantum interference effects. We present a method of inverting the population in a three-level system, without affecting the population in the intermediate state. We also present an all optical implementation of the three-level ladder system, where these effects can be realized.

Physical Review A•Mar 1, 1997•32 citations

Landau-Zener-Stuckelberg interferometry in multilevel superconducting flux qubit

Xueda Wen, Yiwen Wang, Shanhua Cong +7 more

Landau-Zener-Stuckelberg interferometry has been extensively investigated in quantum two-level systems, with particular interests on artificial system such as superconducting flux qubits. With increasing the driving field amplitude, more energy levels will be involved into the quantum evolution, which results in population inversion and many interesting interference patterns. These interference patterns can be used to obtain the parameters characterizing the system and probe dephasing mechanisms of the qubit. Most recently, experiments have been extended to the regime with higher-frequency and larger-amplitude driving field, in which the interference pattern exhibited more complicated characteristics. In this article, we give a universal description of the characteristics observed in both low-frequency and high-frequency regimes. Besides explaining the already observed experimental results, our theoretical model predicted many interesting phenomenon, which can be demonstrated by future experiments.

arXiv:1003.2025•Mar 10, 2010•2 citations

Landau–Zener–Stückelberg Interference in Nonlinear Regime*

Tong Wu, Yuxuan Zhou, Yuan Xu +2 more

Landau–Zener–Stückelberg (LZS) interference has drawn renewed attention to quantum information processing research because it is not only an effective tool for characterizing two-level quantum systems but also a powerful approach to manipulate quantum states. Superconducting quantum circuits, due to their versatile tunability and degrees of control, are ideal platforms for studying LZS interference phenomena. We use a superconducting Xmon qubit to study LZS interference by parametrically modulating the qubit transition frequency nonlinearly. For dc flux biasing of the qubit slightly far away from the optimal flux point, the qubit excited state population shows an interference pattern that is very similar to the standard LZS interference in linear regime, except that all bands shift towards lower frequencies when increasing the rf modulation amplitude. For dc flux biasing close to the optimal flux point, the negative sidebands and the positive sidebands behave differently, resulting in an asymmetric interference pattern. The experimental results are also in good agreement with our analytical and numerical simulations.

Chinese Physics Letters•Dec 1, 2019•5 citations

Revealing the system-bath coupling via Landau-Zener-Stückelberg interferometry in superconducting qubits

Ana Laura Gramajo, Daniel Domı́nguez, María José Sánchez

In this work we propose a way to unveil the type of environmental noise in strongly driven superconducting flux qubits through the analysis of the Landau-Zener-St\"uckelberg (LZS) interferometry. We study both the two-level and multilevel dynamics of the flux qubit driven by a $\mathrm{dc}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}\mathrm{ac}$ magnetic field. We find that the LZS interference patterns exhibit well-defined multiphoton resonances whose shape strongly depends on the timescale and the type of coupling to a quantum bath. For the case of transverse system-bath coupling, the $n$-photon resonances are narrow and nearly symmetric with respect to the dc magnetic field for almost all timescales, while in the case of longitudinal coupling they exhibit a change from a wide symmetric to an antisymmetric shape for times of the order of the relaxation time. We find this dynamic behavior relevant for the interpretation of several LZS interferometry experiments in which the stationary regime is not completely reached.

arXiv:1906.03514•Physical review. B./Physical review. B•Aug 5, 2019•6 citations

Landau-Zener-Stückelberg spectroscopy of a fluxonium quantum circuit

Valentín Reparaz, María José Sánchez, Maximiliano Gatto +2 more

In this work, we study the time-averaged populations obtained for a fluxonium circuit under a large amplitude nonresonant periodic drive. We present numerical simulations of the time evolution which consider the multi-level structure of the driven quantum circuit, looking for a realistic modeling closer to experimental implementations. The Landau-Zener-Stückelberg spectra show resonances that can be understood as originated from constructive interference favoring transitions to higher levels. For a truncated two-level system (TLS) the resonance patterns can be interpreted using a simplified description of the avoided crossing that takes into account the dynamic phase accumulated at each operation point. For the multilevel case, we derive an effective two-level Hamiltonian using a Schrieffer-Wolff transformation starting from the Floquet Hamiltonian in the Sambe space. Our study provides predictive insight into experimental outcomes, offering an intuitive interpretation that could also support the implementation of fast-non-adiabatic single-qubit gates and entangling protocols.

arXiv:2504.21691•Physical review. B./Physical review. B•Jul 23, 2025•2 citations
Landau-Zener-St\uckelberg (LZS) interference is a common tool to study various quantum systems. When system is driven forth and back through anticrossings, phases are accumulated coherently, and results in constructive or destructive interference. LZS are widely demonstrated in two-level systems and multilevel systems. Nonetheless, multilevel physics in LZS interference of a multilevel system remains unexplored, since in most of the cases, influence of each anticrossing can be treated separately, thus two-level model is sufficient. Here, we investigate the LZS interference of multilevel systems in quantum dots (QDs), and propose a scheme to realize an effective model from the complicated energy levels. By employing this model, we study the physics in multilevel system such as Autler-Townes splitting (ATS), electromagnetically induced transparency and coherent population trapping (CPT) etc., and reveal their unique behaviors in our scheme. Specifically, possible improvement for present two-qubit gate in QDs and noise-robust quantum gates are proposed. The theoretical consideration we present is rather general, and thus is in principle valid for other quantum systems with the similar energy structure.
Landau-Zener (LZ) transition has received renewed interest as an alternative approach to control single-qubit states. An LZ transition occurs when a system passes through an avoided crossing that arises from quantum mechanical coupling of two levels, taking the system to a coherent superposition of the two states. Then, multiple LZ transitions induce interference known as Landau-Zener-Stückelberg (LZS) interference whose amplitude strongly depends on the velocity or adiabaticity of the passage. Here, we study the roles of LZ transitions and LZS interference in coherent charge oscillations of a one-electron semiconductor double quantum dot by time-domain experiments using standard rectangular voltage pulses. By employing density matrix simulations, we show that, in the standard setup using rectangular pulses, even a small distortion of the pulse can give rise to LZ transitions and hence LZS interference, which significantly enhances the measured oscillation amplitude. We further show experimentally that the nature of the coherent charge oscillations changes from Rabi-type to LZS oscillations with increasing pulse distortion. Our results thus demonstrate that it is essential to take into account LZS interference for both precise control of charge qubits and correct interpretation of measurement results.
The excitation amplitude after multiple crossings is not a mere product of Landau-Zener transition probabilities at each crossing, due to coherent evolution of the system in between crossings. In the three-level ladder system, the trapping of population by frequency modulated fields ensures coherent evolution, and inclusion of phase effects for population redistribution after multiple crossings becomes necessary. The relative phase accumulated by various adiabatic states as they evolve along different paths is tailored to show the existence of quantum interference effects. We present a method of inverting the population in a three-level system, without affecting the population in the intermediate state. We also present an all optical implementation of the three-level ladder system, where these effects can be realized.
Landau-Zener-Stuckelberg interferometry has been extensively investigated in quantum two-level systems, with particular interests on artificial system such as superconducting flux qubits. With increasing the driving field amplitude, more energy levels will be involved into the quantum evolution, which results in population inversion and many interesting interference patterns. These interference patterns can be used to obtain the parameters characterizing the system and probe dephasing mechanisms of the qubit. Most recently, experiments have been extended to the regime with higher-frequency and larger-amplitude driving field, in which the interference pattern exhibited more complicated characteristics. In this article, we give a universal description of the characteristics observed in both low-frequency and high-frequency regimes. Besides explaining the already observed experimental results, our theoretical model predicted many interesting phenomenon, which can be demonstrated by future experiments.
Landau–Zener–Stückelberg (LZS) interference has drawn renewed attention to quantum information processing research because it is not only an effective tool for characterizing two-level quantum systems but also a powerful approach to manipulate quantum states. Superconducting quantum circuits, due to their versatile tunability and degrees of control, are ideal platforms for studying LZS interference phenomena. We use a superconducting Xmon qubit to study LZS interference by parametrically modulating the qubit transition frequency nonlinearly. For dc flux biasing of the qubit slightly far away from the optimal flux point, the qubit excited state population shows an interference pattern that is very similar to the standard LZS interference in linear regime, except that all bands shift towards lower frequencies when increasing the rf modulation amplitude. For dc flux biasing close to the optimal flux point, the negative sidebands and the positive sidebands behave differently, resulting in an asymmetric interference pattern. The experimental results are also in good agreement with our analytical and numerical simulations.
In this work we propose a way to unveil the type of environmental noise in strongly driven superconducting flux qubits through the analysis of the Landau-Zener-St\"uckelberg (LZS) interferometry. We study both the two-level and multilevel dynamics of the flux qubit driven by a dc+ac\mathrm{dc}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}\mathrm{ac}dc+ac magnetic field. We find that the LZS interference patterns exhibit well-defined multiphoton resonances whose shape strongly depends on the timescale and the type of coupling to a quantum bath. For the case of transverse system-bath coupling, the nnn-photon resonances are narrow and nearly symmetric with respect to the dc magnetic field for almost all timescales, while in the case of longitudinal coupling they exhibit a change from a wide symmetric to an antisymmetric shape for times of the order of the relaxation time. We find this dynamic behavior relevant for the interpretation of several LZS interferometry experiments in which the stationary regime is not completely reached.
In this work, we study the time-averaged populations obtained for a fluxonium circuit under a large amplitude nonresonant periodic drive. We present numerical simulations of the time evolution which consider the multi-level structure of the driven quantum circuit, looking for a realistic modeling closer to experimental implementations. The Landau-Zener-Stückelberg spectra show resonances that can be understood as originated from constructive interference favoring transitions to higher levels. For a truncated two-level system (TLS) the resonance patterns can be interpreted using a simplified description of the avoided crossing that takes into account the dynamic phase accumulated at each operation point. For the multilevel case, we derive an effective two-level Hamiltonian using a Schrieffer-Wolff transformation starting from the Floquet Hamiltonian in the Sambe space. Our study provides predictive insight into experimental outcomes, offering an intuitive interpretation that could also support the implementation of fast-non-adiabatic single-qubit gates and entangling protocols.